Classical simulation of quantum circuits by dynamical localization: analytic results for Pauli-observable scrambling in time-dependent disorder

Abstract

We extend the concept of Anderson localization, the confinement of quantum information in a spatially irregular potential, to quantum circuits. Considering matchgate circuits, generated by time-dependent spin-1/2 XY Hamiltonians, we give an analytic formula for the out-of-time-ordered correlator of a local observable, and show that it can be efficiently evaluated by a classical computer even when the explicit Heisenberg time evolution cannot. Because this quantity bounds the average error incurred by truncating the evolution to a spatially limited region, we demonstrate dynamical localization as a means for classically simulating quantum computation and give examples of localized phases under certain spatio-temporal disordered Hamiltonians.

Major revision, including improvement of presentation and simplification of Theorem 1; results unchanged. Main text: 5 pages (including references), 2 figures, 1 table. Supplementary material: 12 pages, 1 figure

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• Inversion symmetry of singular values and a new orbital ordering method in tensor train approximations for quantum chemistry
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• Quantum information diode based on a magnonic crystal
• Characterizing quantum gases in time-controlled disorder realizations using cross-correlations of density distributions
• Scrambling and quantum feedback in a nanomechanical system
• Directional scrambling of quantum information in helical multiferroics